A189583 Number of permutations of 1..n with displacements restricted to {-4,-2,0,1,3}

1, 1, 2, 4, 13, 26, 62, 132, 274, 614, 1315, 2955, 6423, 14058, 30838, 67170, 147553, 322304, 706400, 1546128, 3382752, 7408261, 16208271, 35489093, 77672999, 170021833, 372181083, 814611385, 1783211187, 3903138418, 8543748906

Offset

1,3

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = a(n-1) +2*a(n-3) +3*a(n-4) +7*a(n-5) +25*a(n-7) -10*a(n-8) +7*a(n-9) -5*a(n-10) -23*a(n-11) -15*a(n-12) -4*a(n-13) -66*a(n-14) +23*a(n-15) -5*a(n-16) +16*a(n-17) +28*a(n-18) -14*a(n-19) +4*a(n-20) +55*a(n-21) -13*a(n-22) -7*a(n-23) -16*a(n-24) -8*a(n-25) +14*a(n-26) -2*a(n-27) -15*a(n-28) +a(n-30) +3*a(n-31) +a(n-32) -a(n-33) +a(n-35)

Example

Some solutions for n=10
..1....3....3....1....1....1....1....1....5....1....3....5....1....1....1....5
..4....1....1....4....2....2....2....6....2....2....2....1....2....2....6....2
..2....2....2....2....5....3....3....7....3....7....7....2....5....3....3....3
..8....4....4....3....6....8....6....3....1....4....1....6....3....4....4....1
..5....9....5....5....9....4....4....2....9....5....9....9....7....5....2....4
..3....5....8....8....3....5....5....5....8....3....8....3....8....6....5....6
..9....6....7....9....4....6....9....4....4....6....4....4....4....7....9....9
..7...10...10....7....7....7...10...10...10....8....5....7...10...10...10...10
..6....8....6....6....8....9....8....8....6....9....6....8....6....8....8....8
.10....7....9...10...10...10....7....9....7...10...10...10....9....9....7....7

Crossrefs

Sequence in context: A018263 A018587 A163986 * A153936 A027301 A153933

Adjacent sequences: A189580 A189581 A189582 * A189584 A189585 A189586

Keyword

nonn

Author

R. H. Hardin Apr 24 2011

Status

approved